There’s no one perfect guide to whether the market is cheap or not, but here are a few measures that may give you pause.

Take the so-called “Cyclically-Adjusted Price-to-Earnings” ratio, which compares share prices, not simply with one year’s profits, but with average earnings across an economic cycle of about 10 years. (This CAPE is often known as the “Shiller PE” after Yale economics professor Robert Shiller, one of its leading proponents.)

The CAPE has been a pretty good guide for investors over a very long period of time. It told you, correctly, to get out of stocks in the late 1920s, the mid-1960s, and the bubble a decade ago. It told you to buy aggressively after the second world war, and in the “death of equities” period of the 1970s and early eighties.

Over the past century or so, the stock market has, on average, been about 16 times cyclically-adjusted earnings. Today, it’s about 20 times. Make of it what you will. But it’s not cheap.

Or take the lesser-known “Tobin’s q.” A calculation, named for the late economist James Tobin, that compares stock prices with the replacement cost of company assets. It has a very similar track record to the Shiller PE.

The q on the market is about 1 today, says economic consultant Andrew Smithers. The historic average is just 0.64. By this measure, the market would have to fall a third just to reach its average. Again: This is cheap?

Or take another measure, “price to sales.” This compares stock prices to corporate revenues, rather than earnings. The rationale is that sales tend to be less volatile from year to year. This data, from FactSet, goes back to 1984. By this measure, shares certainly look a lot cheaper than they were in 2000 or 2007. But they are still much higher than they were before the bubble began in 1995. Ominously, they are higher today than they were just before the crash of 1987.

Still hungry for more? Consider another measure, “enterprise value to EBITDA.” This compares the value of all company stocks and debts with earnings before interest, taxes, depreciation and amortization–a key measure of operating cashflow. Many companies recently have been levering themselves up, borrowing more in the bond market. But all shares and bonds must, ultimately, be supported by cashflows. By this measure, share prices are still way above levels seen prior to the last 13 years.

Finally, you could try comparing the market value of equities with total U.S. gross domestic product. Once again, that’s been a reasonable guide to some of the great buying and selling opportunities of the past. Data from Ned Davis Research show that U.S. stocks are valued at about 85% of GDP today. The historic average, says Ned Davis Research, has been about 60%.

None of these measures is conclusive. None is perfect on its own. And, critically, none is any kind of guide to short-term movements. The market could jump 1,000 points next year just as easily as it could fall 1,000 points.

There is a constant drumbeat of criticism about market valuation using forward earnings. The most common criticism, that estimates are too optimistic, is open to challenge. If the estimates are too high, why is the beat rate consistently in the 65% range?

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The fans of the Shiller 10-year past earnings method take pride in having solid data. Then they make a wild guess about whether the trend will continue. Those praising this method point to a few notable successes, mostly times when P/E ratios were very low since interest rates were very high.

Those interested in forward earnings are taking the aggregate work of dozens of specialists. If you think they are a little high, you can feel free to add an error range. If you do so, you should look at past data — especially that of recent years.

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These points are blindingly obvious, yet widely ignored.

Here is an offer for anyone who thinks that using ten years of past data is the best method: Send me an email and I’ll show you how to enter a nice football pool. The smart money will welcome you and Dr. Shiller.

I prefer Arends’s conclusion:

One should usually give stocks some benefit of the doubt. After all, over the long term they have produced better returns on average than other assets. From that it follows that they have generally been undervalued in the past.

So maybe today stocks are very expensive. Or maybe they’re just no great bargain. But it is almost impossible to argue that they are very cheap. If this were a great contrarian moment to buy stocks, they’d be very cheap.

Somewhere in my maze of bookmarks I have links to a few other papers that support this. From what I remember, long story short, is that you lose a lot of information using averages, just like its possible to drown in a lake that has an average depth of 1 foot.